This invention relates to imaging systems and methods and in particular to systems and methods for reconstructing acoustic properties of an object using mathematical procedures and acoustic wave data.
In conventional parallel beam transmission tomography, such as utilized in x-ray computed tomography (x-ray CT), for example, the attenuation of a narrow beam of x-rays is measured as this beam probes an inhomogenous medium along many different trajectories. The information contained in these attenuation projections is then used to reconstruct a tomographic image of the medium. The success of x-ray CT (manifested in the resolution and clarity of the images) is fundamentally linked to the very short wavelength of the incident x-ray beam (.degree.1 .ANG.). The scattering effects, in the form of diffraction, refraction, and reflection, of the incident x-ray beam are negligible and the dominating attenuation mechanism is absorption. The lack of diffraction effects in x-ray CT results in quite simplified mathematical reconstruction techniques which are used to produce a quality tomographic image. A review of x-ray CT methods is given in, for example, A. J. Devaney, "A Filtered Backpropagation Algorithm for Diffraction Tomography", Ultrasonic Imaging 4, 336-350 (1982); and R. Mueller et. al., "Reconstructive Tomography and Applications to Ultrasonics", Proc. IEEE 67, 567-587 (1979).
In ultrasonic tomography, the acoustic wavelengths are much longer (.apprxeq.1 mm) and the diffraction effects of the incident acoustic beam by the medium are not negligible. In this case, the attenuation of a sound wave is substantially affected by scattering effects such as diffraction, refraction, and reflection, as well as absorption. The simplified mathematical reconstruction algorithms used in conventional x-ray CT, which tacitly assume that attenuation is due to absorption, are not applicable in this case.
Ultrasonic Diffraction Tomography (UDT) techniques attempt to mathematically reconstruct a tomographic image of a medium from scattered acoustic wave data with full consideration to the scattering effects associated with the much longer acoustic wavelengths involved. This is done by considering the full wave equation with diffraction effects, a much more difficult problem to develop and implement than the geometrical wave approximation used in x-ray CT. UDT techniques attempt to determine the internal structure of an object which is semi-transparent to acoustic waves from a partial or complete set of scattered wave data interrogated at the boundary of the object. A number of these inverse scattering solutions have been theoretically considered, from simplified algorithms which use the Born approximation (E. Wolf, "Three-dimensional Structure Determination of Semi-Transparent Objects from Holographic Data", Opt. Comm. 153-156 (1969)) and Rytov approximations (A. J. Devaney, "Inverse Scattering Within the Rytov Approximation", Opt. Lett. 6,374 (1981)) to computer intensive full-wave reconstruction algorithms (S. Johnson and M. Tracy, "Inverse Scattering Solutions by a Sinc Basis, Multiple Source, Moment Method", Ultrasonic Imaging 5, 361-375 (1983) and references therein).
Prior art patents included Devaney (U.S. Pat. No. 4,598,366) and Johnson (U.S. Pat. No. 4,662,222). The patents of Johnson claim iterative algorithms which form an initial sound speed estimate, calculate the measurement which would be expected from that estimate, and then update the estimate. This process is repeated until a residual error parameter is small enough. The patents of Devaney form an image directly from the data using Born and Rytov inversions with a technique called filtered backpropagation. These prior acoustic methods lack efficiency and therefore require a great amount of computation.
It is therefore an object of this invention to provide a system and method which will efficiently reconstruct an image based on the density and/or the sound speed of a medium.